Fig. 5. Model outputs.

(A) Oceanic crustal carbon content through time (blue) with SD (gray). (B) Carbon flux through time showing change in oceanic crustal carbon storage (blue), mid-ocean ridge degassing (purple), subduction flux into the atmosphere (red), and downgoing subduction carbon destined either for the deep mantle or the lithosphere (cyan) (12) assuming a simple 50-50 split. This ratio is not well known and may be anywhere between 1:3 and 3:1. Oceanic mantle carbon subduction flux is based on scaling today’s flux (12) with subduction zone length (Fig. 2B) through time (orange). (C) High-pass–filtered (cosine arch filter with 60-My width) atmospheric CO₂ (black curve with gray error envelope) and modeled total carbon flux (green) including the relevant components shown in (B) (that is, all but the subducted carbon flux partitioned between the lithosphere and the convecting mantle); light red bars indicate bandwidths of the main periods of correlation between ~26-My period peaks in atmospheric CO₂ and modeled carbon flux. (D) Spectral coherence of unfiltered atmospheric CO₂ and modeled carbon flux time series (black, with 1 SD error bars; see text for discussion) peaks at 26 and 16 My. The three curves illustrate the coherence based on assuming that 35% (red), 50% (black), or 65% (blue) of subducted carbon degasses into the atmosphere. Note that the coherence at the 26-My period increases with decreasing subducted atmospheric carbon flux, whereas the remainder of the coherence plot is largely unaffected. (E) Power spectra of globally averaged trench migration speeds faster than 30 mm/year of eight global plate models with alternative reference frames [no net rotation model in light blue; models based on paleomagnetic data in dark blue, green, and dark yellow; and all other models based on hotspot tracks—see figure 4 in the study of Williams et al. (28) for details], revealing a dominant 26-My periodicity in trench migration.